Species richness describes the number of species of a given taxon in a given time and space. The energy limitation hypothesis links the species richness of consumer taxa to net primary productivity (NPP) through two relationships: NPP limits a taxon's density, and taxon density limits species richness. We study both relationships with a survey of 15 ground ant assemblages, along a productivity gradient from deserts to rain forests. Ant density (colonies m-2) was a positive, decelerating function of net aboveground productivity (NAP). A stepwise regression suggests that the efficiency with which NAP is converted to ant colonies increases with maximum summer temperature and decreases with precipitation. Ant species richness was a positive decelerating function of density at three spatial scales. This supports the energy limitation hypothesis' assumption that average population densities are higher in environments that are more productive. These two nonlinear functions (NAP-density and density-species richness) combine to create, at a variety of scales, positive, decelerating, productivity-diversity curves for a common, ecologically dominant taxon across the terrestrial productivity gradient. However, variance in the density and diversity explained by NAP decreases with scale, suggesting that energy limitation of diversity predominates at small spatial scales (<1 ha).